Her responsibilities would include such high-profile and hot-topic issues as immigration enforcement, federal disaster response, and airport security.

As a border-state governor, Ms. Napolitano brings experience to the role of immigration enforcement. She vetoed several tough illegal immigration bills put forward by state Republicans. She also supported the comprehensive reform efforts in Washington that were ultimately shot down last year by opponents of illegal immigration.

However, she also was the first governor to call in the National Guard to beef up border patrols. And her state passed a law last year that requires all Arizona businesses to use the federal online database, E-Verify, to confirm that new hires have valid Social Security numbers and are eligible for employment. This has been a cornerstone of the Bush administration’s immigration policy.

“She’s close and personal with a lot of border and immigration issues.… That’s probably the single greatest thing she brings to the mix,” says James Carafano, an expert on homeland security at the Heritage Foundation. “Arizona has done a lot of pioneering stuff [on immigration]: They have mandatory E-Verify across the state, they’ve tried to crack down with workplace enforcement.”

Napolitano’s approach on immigration is fundamentally pragmatic, says Fred DuVal, founding chairman of the think tank Western Progress and a friend of the governor. Her thinking is, “Drop the ideology and let’s talk about what we need to both make the border secure and the relationship with Mexico functional,” Mr. DuVal says. He adds that Napolitano has a close relationship with her counterpart on the other side of the border in the Mexican state of Sonora.

“She is extremely smart, very prepared, and she absorbs policy material aggressively. She’s in command of the subject and the room by the strength of her knowledge and personality. But she does it with a pleasure in governing that’s quite infectious,” DuVal says.

As governor she has also overseen wildfire and flooding disaster relief efforts and worked with the Federal Emergency Management Agency (FEMA), which is now part of the Homeland Security Department.

Congress and a reluctant Bush administration created the department in response to the failures of federal agencies to coordinate effectively in the run-up to the terrorist attacks of Sept. 11, 2001.

From the beginning, critics decried the DHS as an added layer of bureaucracy trying to hold together vastly different agencies including Immigration and Customs Enforcement (ICE) and FEMA. It also came under fire for not prioritizing domestic-security spending based on objective threat assessments and, instead, engaging in pork-barrel politics.

“The Democrats have always been champions of Homeland Security, so in the spirit of Nixon going to China you might see them be able to cut more from Homeland Security than the Republicans could, and reform the department,” says Ivan Eland, a DHS critic and director of the Center on Peace & Liberty at the The Independent Institute in Washington.

But Carafano cautions against changing the structure of DHS. “The bottom line is that the most disastrous thing you could do would be to reorganize the department and start revisioning roles and departments,” he says. “Every time you do one of these churns, the disruptions you cause create all this friction.”

A lawyer by training, Napolitano started in politics as a volunteer adviser to Anita Hill during the confirmation of Supreme Court Justice Clarence Thomas. President Clinton appointed Napolitano as US Attorney for Arizona. She went on to become the state’s attorney general before winning election in 2002 as the state’s first Democratic governor in 12 years.

She has since maintained a high level of popularity, with a Mason-Dixon opinion poll conducted in August showing 66 percent of Arizonans approving of her job as governor.

Napolitano has generally recruited good people, run a tight ship, and been well organized and focused, says David R. Berman, a professor emeritus of political science at Arizona State University.

If she left for Washington, a couple of Arizona Republicans would be helped in the near term. The Secretary of State Jan Brewer would assume the governorship for the two years remaining on her term. It would also remove her ability to run against Sen. John McCain, who announced recently his intentions to run again for Senate in 2010 after losing his bid for president.

Several news organizations reported Thursday that Chicago businesswoman Penny Pritzker, who was Mr. Obama’s national campaign finance chairman, is his leading choice to become secretary of commerce. But an Obama adviser disputed the reports.

Several people mentioned as possibilities for appointments in the Obama administration have long careers as Washington insiders, notwithstanding Obama’s clarion call in his campaign for change in the nation’s capital.